Problem: The perimeter of a rectangle is $32$ centimeters. The width is $7$ centimeters. What is the area of the rectangle?
Perimeter is the distance around a closed figure. We can find the perimeter of a shape by adding all the side lengths. The perimeter is $32}\text{ cm}$ and the width is ${7}\text{ cm}$. $\text{Perimeter}= 32\text{ centimeters}\,$ $\,7\text{ cm}$ $\,7\text{ cm}$ $\begin{aligned} P} &= {l} + {w} + {l} + {w}\\\\ 32} &= {\ell} + 7 + {\ell} + 7 \\\\ 32} &= {\ell} + {\ell} + {14}\\\\ 18&= {\ell} + {\ell} \end{aligned}$ What number can we add twice to get $18$ ? The length of the rectangle is ${9}$ centimeters. Now, we can find the area. $\begin{aligned} \text{Area} &= {\text{length}} \times {\text{width}}\\\\ &= {9} \times {7}\\\\ &= 63\text{ square centimeters} \end{aligned}$ The area of the rectangle is $63$ square centimeters.